Can I install Visual Studio 2005 and 2010 on the same computer? Would it cause any problems?
Yes, you can do so. I have VS 2005, 2008 and 2010 installed on single machine and they all work independently.
However, before doing so, keep in mind that projects made in lower versions can be opened in higher version only once because after that it will be upgraded to higher version but the opposite is not possible, i.e. backward compatibility is possible but forward compatibility is not possible.